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You can just buy the microcontroller and do it yourself from there. Here is a nice example someone did of a simple LED flasher [1] with just 6 parts:

1. An ATmega ATTiny85 microcontroller

2. A socket for that processor

3. A coin cell battery

4. A holder for the battery

5. A resistor

6. An LED

and some wire and solder.

What going with an actual Arduino or Arduino compatible gets you, from a hardware point of view, is a bunch of ready made attachments. For instance, suppose you have some sensor that needs an odd voltage and has weird timing requirements. It will be a lot more convenient to get a shield that has that sensor, and a voltage converter, and something that deals with the weird timing and presents a simple I2C interface to your code than to have to do all that yourself.

There are some EdX courses that you might find useful.

From UTAustinX, "Embedded Systems--Shape the World" [2]. This is a lab-based course where you do 13 or so labs using a TI Tiva Series C Launchpad. That's an 80 MHz ARM Cortex M4 board. Cost for the hardware for the course is $35-$55, depending on if you want to do a couple of the optional labs.